Chadd Bunker says his friends and relatives tell him he drives like an old man. Roll through a stop sign? He would never do that. Exceed the speed limit? Not on your life. He makes three right turns to avoid a left. He can be annoying.

But Mr. Bunker, who is only 48 years old, is no ordinary driver. He recently became one of the proud, lucky few to reach the delivery driver equivalent of Eagle Scout—the United Parcel Service Inc.'s...